
\section{Conclusion}
\vspace{-0.15in}
We introduced a new type of distributed information propagation mechanism,
namely the BRW and analyzed the cover time and partial cover time of BRW in expanders,
which are  used to model and design P2P and overlay networks. We showed that
the the cover time and partial cover time are exponentially faster in BRW compared to the standard
random walk. Since random walks have extensive applications in networks, we hope  BRW will
also be useful, with the additional property of faster coverage. There are several interesting open problems regarding
BRW
that remain to be solved. In general, unlike the standard random walk which has a well-developed theory,
we know little about the properties of BRW in general graphs. For example, what is the worst case cover time of BRW, and how does it vary with the branching factor $k$? It is clear that the cover time is not worse
than a standard random walk, but it will be interesting  to establish tight asymptotic bounds. Furthermore,
it will be interesting to establish and compare the message complexity of BRW with the standard random walk as well as other gossip-based rumor spreading processes. 